The SIFT algorithm has been generalized to 3D volumetric image data in a variety of applications including video processing [1]}, 3D object detection [2]}, and medical image analysis [3]}, [4]}, [5]}, [6]}. Our work here is based on the 3D SIFT-Rank approach [5]}, which is unique in the way local keypoint orientation and descriptors are computed. Keypoint orientations may be parameterized via a suitable representation such as quaternions or 3x3 rotation matrices, are generally determined from dominant gradients of the scale-space \(\nabla I(x,y,z,\sigma )\)  in a scale-normalized neighborhood about the keypoint. The 3D SIFT-Rank method identifies dominant peaks in a discrete spherical histogram of gradient, rather than solid angle histograms [1]}, [4]}, partial 3D orientation information [3]} or principal components of the local gradient[6]}. This allows identification multiple dominant orientations (3x3 rotation matrices) at each keypoint \((x,y,z,\sigma )\) , leading to multiple descriptors per keypoint and providing robustness to noise, rather than single orientations per keypoint[6]}. Descriptors generally encode the scale-space gradient \(\nabla I(x,y,z,\sigma )\)  in neighborhood about the keypoint, following reorientation. The 3D SIFT-Rank method adopts a compact 64-element gradient orientation descriptor, where the local orientation space is sampled according to \(x\times y\times z=2\times 2\times 2=8\)  spatial bins and 8 orientation bins. Other approaches adopt descriptors that are orders of magnitude larger, e.g. 768-elements from \(4^3\)  spatial bins x 12 orientation bins, leading to similar image matching performance at a much greater memory footprint [6]}. Finally, the SIFT-Rank descriptor is normalized by ranking [14]}, offering invariance to monotonic variations in image gradient.
